Page 696 - Lokmanya Tilak Samagra (khand 2)

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48 SAMAGRA TILAK - 2 • VEDANGA JYOTI~HA
kalds is = 133 + 778 + 45 = 956, or deducting 603, equal to 353
only. Therefore the Moon in this case will enter the last parvan
Nak§hatra, after 353 kalds of the parvan day have elapsed.
I have discussed at some length the meaning of the last two
verses, because their right significance, according to my view, has
not, as yet, been pointed out by any one. But though the explanation
be lengthy, yet the rule itself, as will be seen from the examples
above worked out, is quite simple. We first count the ka/as of the
dozen at the rate of 19 per dozen and then proceed to deal with
excess ( una ) pakshas. The rule for the latter purpose may be
generalized as follows. If x be the number of ~na pakshas let a be
equal to integral part of x/2; then 73x will be the lf~ and
4/3 ( 73x) + 9a will represent the kalds at the end of the given
una-paksha, provided that when the amshas corresponding to the
una-paksha either by themselves, or combined with the amshas
for the previous dozen, are equal to 0r exceed half a Nak~hatra
the value of a will receive a corresponding increase. We have
noticed above the Vedanga artifice of taking four-thirds of 73
instead of 98, and compensating for the error by taking four-thirds
of 7, that is, 9 instead of 7, to calculate the kalds from the +r~
previously determined. The following table will show to what
extent the result so obtained deviates from the one calculated
strictly according to the accurate Vedanga elements. In column 1
is given the value of x or the number of the una pakshas; in column
2 the value of a, as well as the increase it receives under the
circumstance noted above. Column 3 ( a) gives the value of
+r~ or 73x, and 3 (b) of 9a; and their total is given in column
3 (c). Column 4 gives the number of kalas if we take 98 instead
4/3 x 73 and 7 instead 9, or calculate according to the formula
98x + 1a; and the last column shows the error introduced, the
sign+ or- respectively showing that the calculated result is greater
or less than the actual by the number following that sign.
The table is calculated for the una-pakshas only; and to
get the actual results, the amshas as well as the kalds at the end
of the previous dozen pakshas will have to be added to the figures
in the Table. But the latter does not affect the error, except when
the value a is increased thereby, in which case the error would
increase by 2. For example, this will happen when the number of
the total pakshas is 17; because in that case 8 amshas of the pre-
vious dozen when added to 55 of the five una give rise to an addi-